Not an unreasonable question at all and have seen it asked on this and other RV forums before. Recycling some of the heat content in the exhaust flue gas is technically possible but you would def. NOT do it by extending a flue pipe under the trailer.
An air-air or air-water heat exchanger could technically be used but would need to be installed outside of the TT exterior wall and not underneath. Lots of things would need to be addressed such as - the high moisture content of the exhaust gas & corrosion; not disrupting exhaust gas flow and keeping it within the manufacturer's parameters; and how you would attach something to the furnace's exhaust/intake vent on the exterior.
To take this a bit further, if camping in cold weather over the winter, you MUST remove moisture in the indoor air. If you don't, you can end up with rot in framing, delamination of the exterior wall (if fiberglass), mold and in some cases water even condensing on the ceiling and dropping like rain. Even a slight amount of moisture in batt insulation can reduce it's R-value significantly and lead to even more moisture issues to deal with. There is an incredible amount of water released into the air by a human body, washing dishes and showering. You will need to crack open roof vents and some windows so you get a cross flow of air through the interior and out the roof vents. This will obviously cool the interior more and will require the furnace to run more. Not an efficient way to remove moisture!
Don't seal up weep holes in windows - you need them to drain away condensation. Seal up holes & penetrations through the floor with spray foam or tuck tape. There will be some heat loss under the bed and through the interior wall of the pass-through compartment. Rigid foam can be used there too.
Dessicant type dryers won't remove enough moisture fast enough. Electric dehumidifiers can be used and work well but make noise and water needs to be drained away or dumped regularly. An air-air heat exchanger is feasible but where to install one. There was a thread a few years back about someone who built his own and can be found
here. Interesting read.
Does the TT have an enclosed underbelly or not? If enclosed, the underbelly space gets heated with a duct or two off the furnace which is a very inefficient way to heat the space and to prevent the tanks and piping from freezing. Not the right time of year to be working under your trailer but if it was, I'd install 1"-2" rigid foam sheets (closed cell type) immediately under the floor and seal cracks and openings with spray can foam. Plumbing lines could be re-routed as needed tight to underside of floor and above the insulation. Then install heating blankets under the tanks and re-install the underbelly coroplast "if so equipped". If you do this, it could make using an electric heater or two more feasible due to reduced heat loss plus will make the floor warmer for your feet.
Instead of sheet plastic skirting I would use sheets of closed cell foam and seal joints with tuck tape. This stuff isn't cheap tho. and might be found on CL if lucky. I've bought a few thousand sq. feet of it from a local building material recycling place for a small fraction of new cost. If you had a way to keep it secured and not blowing away, you could even lay some rigid foam on the roof.
There was an interesting story in Trailer Life a couple of years ago about a guy who solo camped in the Yukon over the winter in an R-Pod in -40F temps. RV.net refuses to work when I try to post a link so copy and paste into your browser: http://www.trailerlife.com/lifestyle/braving-the-yukon/
